$A$ soap bubble in vacuum has a radius of $3 \, cm$ and another soap bubble in vacuum has a radius of $4 \, cm$. If the two bubbles coalesce under isothermal condition,then the radius of the new bubble is ....... $cm$.

There is an air bubble of radius $1.0\,mm$ in a liquid of surface tension $0.075\,N\,m^{-1}$ and density $1000\,kg\,m^{-3}$ at a depth of $10\,cm$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is $....Pa \left( g = 10\,m\,s^{-2} \right)$

$8$ mercury drops coalesce to form one mercury drop. The energy changes by a factor of:

$A$ spherical drop of water has a radius of $1\, mm$. If the surface tension of water is $70 \times 10^{-3}\, N/m$,the difference of pressure between the inside and outside of the spherical drop is ........ $N/m^2$.

$1000$ spherical drops of water each $10^{-8} \ m$ in diameter coalesce to form one large spherical drop. The amount of energy liberated in this process (in joule) is (surface tension of water is $0.075 \ N/m$).

If the excess pressure inside a soap bubble of radius $3 \,mm$ is equal to the pressure of a water column of height $0.8 \,cm$, then the surface tension of the soap solution is ( $\rho_{\text{water}} = 1000 \,kg/m^3, g = 9.8 \,m/s^2$ ).